Due Mar 9, 3:59 AM EDT
Assume that we have a sample space with five outcomes: {ω1,ω2,ω3,ω4,ω5}. Denote probability of outcome ωi by pi, i=1,2,3,4,5. Which of the following collections of numbers pi correctly define probability space?
Consider non-symmetric dice for which probability to get k points is proportional to k, k=1,2,3,4,5,6. (I.e. probability to get 2 is twice as large as probability to get 1.) What is the probability to get 1 point on this dice? Enter proper fraction
Let x be the probability to get one point. Then the probability to get k points is kx. Sum of all probabilities should be equal to 1, therefore, we have an equation: x+2x+3x+4x+5x+6x=1 which is equivalent to 21x=1. Therefore, x=1/21
Consider non-symmetric dice for which probability to get k points is proportional to k, k=1,2,3,4,5,6. (I.e. probability to get 2 is twice as large as probability to get 1.) What is the probability to get less then 3 points? Enter proper fraction.
According to previous question, probability to get 1 point is 1/21 and 2 points is 2/21. The probability to get less then 3 points is a sum of probabilities to get 1 point and to get 2 points.